A UH-1H helicopter of National Airborne Service Corps (NASC) performed the hoist up rescue training, the flight engineer released the wire rope and started to retrieve the rope to hoist personnel after seeing the end of the rope was hooked well with the trainee. Then the helicopter started moving forward slowly, and at the same time the flight engineer kept on retrieving the wire rope. At 30 feet from the ground the flight engineer felt the rope retrieving process was stopped and the rope started to slip down. After inspection flight engineer found that the pulling device could not be controlled, which led the rope to slip downwards and saw the hoisted personnel falling off to the ground. Due to Taiwan Aviation Occurrence Investigation Act, it was classed as an Aviation Occurrence. Taiwan Aviation Safety Council (ASC) shall be responsible to conduct the following investigations on aviation occurrence of Civil aircraft, Public aircraft or Ultra-light Aircraft arises in the territory of the Republic of China. Findings related to possible causes in ASC's final report: "During overhaul the hoist device had a wrong measurement for the axial gap value, which caused the axial gap of the coupling oversized after the assembly. During hoist operation when the coupling face length of the drive gear decreased from 0.074 inch to 0.015 inch, the maximum stress the drive gear wall could take was over the yield strength and damaged; the drive gear could not take the load of the coupling stress from the driven gear and began to slip. The driving gear was over-driven by the load to rotate in the opposite direction, which led the hoisted personnel to fall off." This research intends to find the probable cause of the occurrence from engineering point of view, and proposes material test and finite element analysis (FEA) for Engineering Failure Analysis of the Rescue Hoist Device. At first, ASC checks all the maintenance records of the Rescue Hoist Device and makes sure that no abnormal was found. Following examinations and tests were macro observation and photographic documentation, chemical analysis, hardness testing, metallographic examination, Scanning Electron Microscope (SEM) examination, to determine the root cause of failure. Furthermore the finite element analysis is conducted for stress analysis. The sole purpose of this study is to give some preventions and safety recommendations, and ultimately prevent recurrence of similar failures.